LLM agents execute in an interleaved reasoning-and-action loop, where future tool calls cannot be launched until the current reasoning step completes. This serial dependency inflates end-to-end latency and leaves the model idle while waiting for tool execution. Prior work, Pattern-Aware Speculative Tool Execution (PASTE), mitigates this bottleneck by speculating likely future tool invocations from mined control-flow and data-flow regularities. However, PASTE is tool-centric and speculates only individual invocations rather than bounded future branches. We propose B-PASTE, a beam-aware extension that lifts speculation from single tools to local branch hypotheses under strict resource constraints. B-PASTE maintains a bounded beam of future execution subgraphs, ranks them by expected critical-path reduction rather than raw execution probability, and schedules only high-value branch prefixes on transient slack resources. It explicitly models co-run interference, downstream unlock value, and state-safety constraints, enabling the system to prioritize serial fast-path execution when early completion unlocks valuable future work, while still exploiting safe parallelism under low contention. This design is especially important for edge-side deployments, where speculative work must not steal scarce resources from latency-critical authoritative execution. Preliminary internal testing on Thor-class edge environments shows up to 1.4X end-to-end speedup, suggesting that branch-aware speculative execution remains effective even under tight resource budgets.